Lecture 52 - What you should have learned last time What...

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CEE 260: Environmental and Sustainable Engineering Principles Financial Comparison of Technology Options Lecture# 52 Reading: Rubin Ch 13: pages 553-583 What you should have learned last time What are the basic terms used in finance? • Interest • Present Value / Future Value • Annuity / Uniform Series of Payments How are basic finance calculations performed? How can two technology options be compared financially via present value calculations? Engineering Economic Cost Parameters Cost Factors in Economic Analysis Cash Flow Examples Up front capital costs versus annual operating and management costs Addition of Present and Future Values The PV of a stream of future cash flows is equal to the sum of the PV value of each of the cash flows. (Reverse for FV) Example: Assume an interest rate of i = 8% and calculate the PV of the following cash flows: Year Cash Flow Years to Discount: n Present Value 0 -$1000 0 -$1,000 1 $200 1 $185.19 2 $1500 2 $1,286.01 3 $2000 3 $1,587.66 Present Value Equals $2,058.86 () n i F P + = 1
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Annuities, or Uniform Series of Payments (U) A special case of PV or FV addition is the case of annuities. An annuity is a set of identical (i.e., uniform) cash flows, one each year (or period). The FV of an n-year regular annuity where i is the interest rate and U is the payment value per period The PV of an n-year annuity: () + = i i U F 1 1 n + × = i i U P n 1 1 n i F P + = 1 Perpetuities, or Infinite Uniform Series A perpetuity is simply a set of equal payments that are paid forever. If the yearly payment is $U, then the present value of the perpetuity is: The value of a perpetuity can be used to estimate the value of similar long-lived annuities. For example assume a 10% interest rate and compare the following two alternatives: A: A perpetuity of $100. B: A 30 year annuity of $100. ( ) + × = i i U P n 1 1 i U P $ = 69 . 942 $ 1 . 1 1 1 1 . 100 $ 30 = + × = B PV $1,000 0.1 $100 PV A = = ICP #41 Life Cycle Costs of Technology Purchase Suppose we needed to decide between two different technologies that will do the same job equally well.
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This note was uploaded on 04/17/2008 for the course CEE 260 taught by Professor Kimf.hayes during the Fall '06 term at University of Michigan.

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Lecture 52 - What you should have learned last time What...

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